Bernt,  I'm not familiar with your particular machine, but
oscillation in general can be changed or eliminated by increasing
or decreasing mass (and thus the resonant frequency) of the moving
parts.  Try attaching, with duct tape, a hunk of metal like a large
nut or fishing weight on one or the other parts and see if it
improves or gets worse.

I was also thinking that if the spill opening was choked a little,
perhaps by surrounding the valve with a loose felt pouch attached
to the larger board, the dynamics might change enough to stop the
oscillation.

Greg Graham